Amplitudes of three-dimensional waves in a nonisothermal falling liquid film

The amplitudes of three-dimensional (3D) waves in a water film flowing down a vertical plate with a local heater have been measured. Thermocapillary forces that arise on heating lead to the formation of rivulets separated by thin-layer troughs, with 3D waves propagating over the crests of rivulets. The film thickness and 3D wave amplitudes on the heater grow with increasing heat flux density and distance downstream the flow, but the relative wave amplitude remains unchanged. In the heated regions between rivulets, the relative amplitude of waves increases with decreasing average thickness (or local Reynolds number). Analysis of results obtained for large Reynolds numbers showed that the relative amplitudes of waves in the regions between rivulets at high heat flux densities are much greater than those for small Reynolds numbers in isothermal falling films.     

Marangoni effect on wave structure in liquid films

Liquid films are encountered in space systems as well as in numerous industrial processes and everyday life. The present work is a part of the preparation of the SAFIR experiment of the European Space Agency onboard the International Space Station. Wave characteristics of the water film flow over a vertical or an inclined plate with a heater have been studied. The fluorescence method was used to measure local instantaneous film thickness. In addition to measure wave characteristics eight capacitance sensors were located as a line across the flow. The process of rivulet formation in a heated film was registered. Two zones of the heat flux effect on liquid film deformation were distinguished. At low heat fluxes, the film flow is hardly deformed. At high heat fluxes the thermocapillary forces provide formation of rivulets and a thin film between them. The measured values of the distance between rivulets depend slightly on the plate inclination angle. It was found that for a positive temperature gradient along the flow, heating may increase the wave amplitude because thermocapillary forces are directed from the valley to the crest of the wave. This effect was shown in the interrivulet zone, where relative wave amplitude and Marangoni number increase with a rise of the heat flux density.     

The Effect of Wave Formation and Wetting Angle on the Thermocapillary Breakdown of a Falling Liquid Film

An experimental investigation is performed of the breakdown of a liquid film flowing down a vertical plate with a heater sized 150×150 mm. The main parameters which are varied in the experiment are the Reynolds number Re = 0.47 to 331 and the heat flux q = 0 to 1.92 W/cm². It is found that the effect of the heat flux on the wave motion of the liquid film causes the formation of a jet flow. Dry spots are formed in the region of thin film between the jets. For the purpose of investigating the effect of wave formation on the film breakdown, the distance between the nozzle and heater is varied from 41.5 to 200 mm. It is found that the distance between the nozzle and heater defines the hydrodynamics of the liquid at relatively low heat fluxes, but has no appreciable effect on the heat flux at which the film breakdown occurs. Different working liquids and coatings of the working surface are used in the experiments to investigate the effect of the wetting angle on the film breakdown. The equilibrium wetting angle is measured by the "bubble" method. No effect of the equilibrium wetting angle on the nonisothermal breakdown of the film was revealed.     

Experimental study of the wave flow of a liquid film on a heated surface

The wave flow of a water film over the surface of a vertical plate with a 150×150-mm heater has been experimentally studied. The action of heat flux on the wave flow of the liquid film is manifested by the formation of periodic flowing rivulets separated by thin film regions. The thickness of the film between rivulets was measured using a fiber optical reflection probe. As the heat flux grows, the average film thickness h continuously decreases. However, when the thickness reaches h≈0.5 h₀, where h₀ is the value given by the Nusselt formula for a laminar liquid film, the film exhibits spontaneous rupture. It was found that, as the local flow rate decreases, the wave amplitude in the region between rivulets drops more rapidly than expected according to the laws of “cold hydrodynamics.”     

Evolution of the temperature field at the three-dimensional wave front in a heated liquid film

An experimental study of the transformation of three-dimensional waves into thermocapillarywave structures in the flow of water film on a vertical plate with a heater was carried out using the fluorescent thickness measurement technique and a high-speed infrared recording technique in order to measure the temperature field on the liquid film surface. It was shown that the temperature disturbances occur in the residual layer of the wave film. Then, as the film flows along the heater, temperature inhomogeneities appear transverse to the flow at the three-dimensional wave front; and these inhomogeneities cause deformation of the liquid film and formation of rivulet due to the action of thermocapillary forces.     

Thermal entry length in falling liquid film

The variation in thermal entry length (TEL) in a heated liquid film flowing down a vertical plate has been experimentally studied for high Reynolds numbers of the flow. Even at low heat fluxes, zones with a temperature exceeding the initial temperature of the film are formed at a distance of ∼7 mm from the upper edge of the heater in the region between rivulets, which is formed between the crests of developed three-dimensional synchronous waves. In rivulets passing along the crests of these waves, the TEL is greater, but it rapidly decreases with increasing heat flux density.     

Heat transfer in a subcooled evaporating liquid film

An investigation is performed of heat transfer in films of water and FC-72 liquid falling down a 60×120 mm heater. Heat transfer mode maps are constructed. Zones of structure formation and regions of emergence of breakdown of liquid film are identified, as well as regions of boiling in jets. An averaged coefficient of heat transfer was used in analyzing the experimental data. It is demonstrated that thermocapillary forces have a complex and ambiguous effect on heat transfer. The emergence of extensive stable dry spots causes a decrease in the average coefficient of heat transfer. On the other hand, an increase in the path length of film and in the amplitude of wave motion leads to the washing out of the dry spots and to an increase in the relative intensity of heat transfer. The regularities of heat transfer in the region of flow of film with breakdowns for weakly and intensely evaporating liquids differ significantly. An enhancement of heat transfer is observed under conditions of significant evaporation during structure formation in the thermocapillary mode.     

Explosive collapse of vapor film under conditions of intensive heat fluxes

The stability is investigated (linear and nonlinear analysis) of the interface between a thin vapor film and a layer of liquid in the presence of a steady heat flux from a metal surface heated to a high temperature to the vapor film and then from vapor to subcooled liquid. In view of thermal disequilibrium which takes into account the temperature dependence of saturation pressure, boundary conditions on the vapor-liquid interface are derived, which generalize the known correlations on the free surface of liquid in the gravity field. A number of new effects arise in the problem under consideration, as distinct from the classical problem. The thermal processes, which occur on the phase boundary and are possible in the absence of the force of gravity as well, lead to the generation of weakly decaying periodic waves of low amplitude, whose velocity may exceed significantly that of gravity waves. The heat flux through the interface may cause on this surface periodic waves of small length (ripple) which are not capillary. The processes of phase transition on the interface are capable of providing for the stability of vapor film under the layer of liquid in the gravity field. Along with periodic waves and solitons, the mode of explosive instability may arise in the nonlinear stage because of a weak variation of the film thickness, where the amplitude of an initially low-amplitude plane wave rises to infinity during a finite period of time.     

Control over the formation of structures in a heated liquid film

An experimental investigation is performed of the impact made by artificial disturbances on the formation of structures under conditions of flow of water film on a vertical plate with a heater. The fluorescent method is used for measuring the film thickness. It is found that artificial disturbances on the surface of liquid film may cause a significant variation of the spacing between jets, and the scenario of evolution of wave pattern depends on their intensity. Artificial disturbances on the film surface cause the spacing between jets to decrease from values corresponding to the thermocapillary-wave mode of formation of jets to values close to those of spacings typical of the thermocapillary mode. In so doing, the spacing between jets may be varied at higher values of Reynolds number than is the case in the thermocapillary mode. It is demonstrated that it is possible to control the formation of structures on the surface of a heated film of liquid, and the conditions of maximal effect of artificial disturbances are determined.     

Controlling interaction of hydrodynamic waves with thermocapillary instability in falling liquid film

The interaction of hydrodynamic-wave and thermocapillary perturbations in a locally heated water film flowing down a vertical plate has been experimentally studied using a high-speed IR imager. It is established that, in the presence of fairly high heat fluxes, artificial disturbances can significantly influence the formation of wave structures and the wave flow in the liquid film. Depending on the parameters of waves passing the heater, various scenarios of their transformation into rivulets are possible.     

Axisymmetric waves in electrohydrodynamic flows

The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet inside a hollow cylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial waves influenced by surface tension and electrical stresses are computed in both cases. The computations are capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that, for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case the electric field promotes bubble formation, all other parameters being equal.     

The Effect of Three-Dimensional Deformations on Local Heat Transfer to a Nonuniformly Heated Falling Film of Liquid

An experimental investigation is performed of heat transfer under conditions of flow of a water film on a vertical surface with a heater 150×150 mm in size in the range of the Reynolds number values from 1 to 45. A map of modes of flow of the liquid film is plotted, and regions of heat transfer are identified. Data are obtained on the longitudinal coordinate dependence of the heater wall temperature and of the local heat flux on the symmetry axis of the heater. Local coefficients of heat transfer are measured. The experimental data are compared with the results of numerical calculations for a smooth film. The effect of the forming of jet flows on heat transfer to the liquid film is analyzed.     

Thermal entry length in a falling liquid film at high reynolds numbers

Using the fluorescence and the infrared technique of thickness and temperature measuring, experimental study is performed on variation of the thermal entry length in a falling water film at high Reynolds numbers. The data obtained by means of a high-speed infrared camera show that, in the interrivulet area occurring between the crests of the developed synchronous 3D waves, even at low heat fluxes, at distances of 7–10 mm from the upper heater edge, zones are formed with the temperature above the initial film temperature. The thermal entry length is shown to be larger within the area of the rivulets forming over the synchronous 3D wave crests, but it decreases rapidly with the heat flux density increase. Analysis of the film thickness data obtained by the fluorescent technique shows that, within the areas between the synchronous 3D waves, the averaged film thickness is less. Respectively, the values of the local film Reynolds number decrease, as do the distances to the localities of the temperature non-uniformities. In those places, even at relatively low heat fluxes, the influence of the thermo-capillary force takes place thus causing a significant decrease in the thermal entry length.     

Heat Transfer in Subsonic Flows of Dissociated Nitrogen: HF Plasmatron Experiment and Numerical Simulation

Experiments on heat transfer in subsonic jets of dissociated nitrogen have been carried out on a IPG-4 induction plasmatron. The heat fluxes to copper, stainless steel, nickel, graphite, and quartz surfaces at the stagnation point of a water-cooled cylindrical flat-faced model 20 mm in diameter and dynamic pressures have been measured at a pressure of 50 hPa in the test chamber and a power of 35–65 kW of the HF generator. The experiments showed the influence of surface catalytic properties on the heat flux in relation to the nitrogen atom recombination. In the conditions of the experiments, a numerical simulation of nitrogen plasma flows in the discharge channel of plasmatron and the subsonic dissociated nitrogen jet flow around the cylindrical model has been carried out. The experimental and calculated data on heat fluxes to cooled copper, stainless steel, nickel, graphite, and quartz surfaces are compared. The quantitative catalyticity scale of the studied materials in relation to the heterogeneous recombination of nitrogen atoms is established.     

Development of Crisis Phenomena in Falling Wavy Liquid Films at Nonstationary Heat Release

This paper deals with investigation results on crisis phenomena for nonstationary heat release in falling liquid films. According to the experimental results, in the studied range of irrigation degree alteration (Re _in = 60–1,690), parameters, characterizing decay of the falling liquid film with stepped heat release (distribution of time of boiling incipience along the liquid film, velocities of movable boundaries in the boiling-up and drying fronts), depend complexly on the Reynolds number, wave characteristics and heat flux density. The time of boiling incipience at stepwise heat release was simulated numerically with consideration of intensive evaporation development from the free surface of a laminar-wave film, transportation of large wave crests at typical process times and influence of the convective component of heat transfer. It is shown that the convective component of heat transfer in the wave liquid films and film thinning because of intensive evaporation provide a significant increase in the time of boiling incipience for the given heat fluxes under the conditions of nonstationary heat release. It is also revealed that for low densities of the heat flux at decay of a laminar-wave liquid film occurs with formation of metastable regular structures with liquid rivulets and large-scale dry zones between them. When loading thermal impulses of high intensity, film decay is determined by dynamic characteristics of propagation of the self-maintained front of liquid boiling-up and the shape of structures, formed during its development.     

Deformation of horseshoe-shaped waves in heated falling liquid film

The formation of rivulets on the surface of a nonisothermal liquid film flowing down a vertical plate heated in the bottom part has been experimentally studied. The distances between rivulets and the film thickness are determined as functions of the Reynolds number and the heat flux density. It is established that heating of the falling film leads to deformation of the horseshoe-shaped waves.     

Effect of gas stream swirls on the instability of viscous annular liquid jets

Summary. A linear temporal instability analysis has been carried out for a viscous annular liquid jet moving in two swirling gas streams of unequal velocities with the gas stream swirling motion represented by free-vortex rotation. It is found that two modes of unstable surface waves exist, the para-sinuous and para-varicose mode. The results of the two limiting flow situations, which are a cylindrical liquid jet in a swirling gas stream and a swirling gas jet in a liquid stream, indicate that their instabilities are associated with the para-varicose mode on the outer interface and para-sinuous mode on the inner interface of the annular liquid jet, respectively. It is shown that the centripetal force induced by the inner gas stream rotation is destabilizing and enhances the jet instability, while the centripetal force produced by the outer gas stream rotation is stabilizing and reduces the instability of annular liquid jets. It is interesting to find that for a para-varicose mode an increase in the outer gas rotation not only reduces the upper cut-off wave number, but also increases the lower cut-off wave number, leading to the significant reduction in the unstable wave number range. The stabilizing effect of the outer gas rotation is much more significant for para-varicose mode, and the destabilizing effect of the inner gas rotation is much more influential for para-sinuous mode. In general, the para-sinuous mode has a much larger growth rate and is predominant in the annular liquid jet breakup process. Therefore, increasing the inner gas stream rotation can significantly enhance the breakup of annular liquid jets for practical spray applications.     

Nonstationary effect of artificial perturbations on a nonisothermal falling liquid film

The effect of nonstationary artificial perturbations on the formation of rivulets on the surface of a nonisothermal liquid film flowing down a vertical plate with a heater has been experimentally studied. The film thickness was measured using a fluorescent technique. It is demonstrated that, using periodic perturbations, it is possible to change the distance between rivulets with time. An increase in the wave amplitude at the front of a propagating perturbation has been observed. It is established that the wave amplitude growth and the liquid mass transfer across the flow lead to the washing of dry spots downstream the heater.     

The Effect of Gravity and Shear Stress on a Liquid Film Driven in a Horizontal Minichannel at Local Heating

The present study is focused on the investigation of gravity effect on thermocapillary deformations in a film flowing under action of co-current gas flow, which creates the tangential force on the gas–liquid interface. The influence of local heating intensity on the heater at a substrate is also investigated. Effects of surface tension, temperature dependent viscosity and thermocapillarity are taken into account. Investigations have shown that gravity has a significant effect on the film deformations and pattern. Decreasing of gravity level leads to a flow destabilization. 3D liquid film pattern noticeably changes in spanwise direction. Increasing of heat flux leads to increasing of liquid film deformations. Dependence of film thinning on heat flux is strongly nonlinear. The most dangerous deformations (regions of minimum film thickness with possible disruption of liquid) take place behind the downstream edge of the heater at any gravity conditions.     

An experimental modeling of gravity effect on rupture of a locally heated liquid film

This study deals with the formation of dry patches in a subcooled liquid film flowing over a locally heated plate at small positive and negative plate inclination angles with respect to the horizon. Prior to film rupture appreciable thermocapillary deformations of the film surface appear, growing with the heat flux. Upon reaching a threshold heat flux the film rupture occurs. By means of high speed imaging it is found that the process of rupture involves two stages: 1) abrupt film thinning down to a thin residual film on the heater; 2) rupture and dryout of the residual film. As the plate inclination angle is reduced the threshold heat flux required for film rupture weakly decreases, however when the angle becomes negative the threshold heat flux begins to rise dramatically, which is associated with an increase of the stabilizing hydrostatic effect due to the growth of the film thickness. The characteristic time of rupture decreases as the threshold heat flux increases. At nucleation of the dry patch the speed of contact line can be as high as 220 mm/s. The results obtained, apart from their intrinsic importance for ground-based applications, can also be of interest for microgravity research as a film flow with different relative contribution of inertia, hydrostatic and thermocapillary forces is considered.